1.
Simplify the following leaving your answer in factorial notation if possible.
a )654!

b
)(1,)
P
nn
10

c) 
2

d)
__________________
__________________
__________________
75!
71!
___________________
(2)!
n
n!
2.
Simplify
3.
How many three digit numbers can be formed without repetition? __________________
4.
Evaluate 0! + 1! x 3! + C(n,n)
5.
Find the number of arrangements of the letters in the word BORAT if:
6.
7.
8.
___________________
a)
there are no restrictions
_______________
b)
the word must start with RA
_______________
How many teams of 4 can be made from 6 boys and 8 girls if:
a)
there are no restrictions
__________________
b)
there are no boys on the team
__________________
How many five digit PIN numbers can be formed if:
a)
repetition is not allowed
b)
the number is odd and repetition is not allowed
c)
the number must be greater than 40000 and repetition is not allowed
How many ways can a set of 6 CD’s be arranged if:
a)
they must be in alphabetical order
b)
they are not in alphabetical order
9.
How many arrangements of the word MATHEMATICS can be made if:
a)
the new word must begin with a vowel and end with a consonant
b)
the vowels must be all together
10.
How many arrangements can be made for a personalized licence plate if you can use
numbers and letters and can have a maximum of six characters on the plate?
11.
a) each student’s lock has 60 numbers on the dial. How many possible combinations are
there for a lock?
b) what is the minimum number of numbers on the dial of a “combination” lock for a
school as large as Frontenac with 1050 students?
12.
A six person committee is to be chosen from 10 boys and 8 girls. How many ways can a
committee be chosen if:
a)
there must be at least one boy on the committee
b)
the president, secretary and treasurer (all girls), must be on the committee
13.
14.
A bag of poker chips contains 4 white, 6 red and 3 blue. How many different selections
of poker chips from the bag are possible assuming you must select at least one poker
chip?
n

5(,3)24
Pn  
Solve for n, where nN

4
